There are two triangles: a small one to the left and a big one, which includes the small one. They both have a common angle (the leftmost angle) and since (we can assume) the two columns meet the floor at right angles, they both have two equal angles. This means they are similar (AAA).
Let the distance of the base of the stairs to the tallest column be d.
Because matching sides of similar triangles are in the same ratio, 4 / 6 = d / (6 + 12) 4 / 6 = d / 18 (4 * 18) / 6 = d d = 12
